1
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0answers
38 views

Graphene Chern number for Dirac nodes

Why do we add winding number at two Dirac nodes to determine topological phase?
2
votes
1answer
104 views

Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene

Borrowing from Laughlin's argument on quantum Hall effect, Kane and Mele argued why there must be edge states in graphene with spin-orbit coupling in one paragraph, which is above the one with ...
4
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1answer
130 views

How to derive electron number equation of Bogoliubov Hamiltonian using thermodynamic relations.

My question arise from this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. I will describe my question in detail so that you might not need to look into that ...
1
vote
1answer
49 views

'Pseudo-Relativistic' behavior in Graphene

I've read that electrons in Graphene behave 'pseudo-relativistically'; what does this mean? how do they behave differently from electrons in other materials?
1
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0answers
59 views

Symmetry argument about degeneracy of graphene energy band at Dirac point

This question is very related to the thread here. In the answer given by @BebopButUnsteady , the statement is that as long as the inversion and time-reversal symmetry are respected, the Dirac points ...
3
votes
1answer
106 views

Superconductivity in graphene with spin orbital coupling, is it proper to let the order parameter on two sub-lattice equal?

I am reading this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. Considering just the first part of the article, where a negative-U Hubbard model with the ...
6
votes
1answer
119 views

Material implementations of the holographic principle

I'm afraid this question is a little too open-ended, but bear with me while I find a better formulation. carbon allotropes (like fullerenes and graphene) are regular patterned. Conduction bands of ...
2
votes
1answer
283 views

valence bands in graphene

In Graphene, each carbon use 3 electrons to form sp2 bonding with neighboring, and in a unit cell, there are 2 carbon atoms, so at least these 6 electrons contribute to 6 valence bands. Then my ...
6
votes
3answers
536 views

Graphene +1 extra carbon bond

I'm not a physicist just a curious mind, so please go easy! I was just watching a BBC Horizon Documentary that featured a piece on the recently discovered material Graphene. One of the facts ...
3
votes
1answer
206 views

Graphene with a disclination and the spin-orbit coupling

I am trying to follow the methods used in this paper (http://arxiv.org/pdf/1208.3023.pdf) to construct the Hamiltonian of a graphene cone, but taking into account the spin-orbit coupling. The paper ...
3
votes
2answers
247 views

What limits the maximum attainable Fermi Energy for a material experimentally?

Either through doping or gating. What are some good terms to search for if I'm looking for some experimentally obtained values for particular materials? I'm particularly interested in what the limit ...
2
votes
1answer
197 views

What are the statuses of Silicene and Graphene for real world circuit production?

A lot of hype is out there about both of them (especially the latter) and I was wondering if there is more concrete information about them other than the news IBM posted on a circuit 2 years ago and ...
3
votes
2answers
595 views

Exact diagonalization of graphene's tight binding Hamiltonian

While directly diagonalize graphene's tight binding Hamiltonian, which is numerical. We have to use a finite-sized graphene. So how to deal with boundary conditions? The usual solutions are zigzag or ...
1
vote
1answer
3k views

Effective Mass and Fermi Velocity of Electrons in Graphene:

In graphene, we have (in the low energy limit) the linear energy-momentum dispersion relation: $E=\hbar v_{\rm{F}}|k|$. This expression arises from a tight-binding model, in fact $E =\frac{3\hbar ...
3
votes
2answers
356 views

Thomas-Fermi approximation and the dielectric function (+ small bit on graphene)

1) With the dielectric function, which is a function of wavenumber and frequency,how is it possible to take the limit of either to zero without changing the other one? I thought that frequency and ...
0
votes
1answer
223 views

Why is the spinor wave function of graphene what it is?

Why is the spinor wave function of graphene $[e^{-i\theta/2}, e^{i\theta/2}]$? Could it be $[e^{-i\theta/}, 1]$?
2
votes
1answer
819 views

Helicity and Pseudospin in Graphene

The Hamiltonian for graphene at $\vec{k}$ away from the $K$ point is proportional to $$ \vec{\sigma} \cdot \vec{k} =\begin{pmatrix} 0 & k_x - i k_y \\ k_x + i k_y & 0 \\ \end{pmatrix} = k ...
5
votes
0answers
230 views

Significance of Dirac cones in condensed matter physics

In condensed matter physics, Dirac cones can be found in graphene, topological insulators, cuprates, and iron-pnictides. This means that electrons behave as massless particles near the Dirac points. ...
5
votes
1answer
371 views

Graphene Moebius Strip

I'm refering to the Paper: PHYSICAL REVIEW B 80, 195310 (2009) "MoĢˆbius graphene strip as a topological insulator" Z. L. Guo, Z. R. Gong, H. Dong, and C. P. Sun. The paper is also available as a ...
5
votes
1answer
880 views

Tight Binding Model in Graphene

I'm following a calculation done by a guy who's done it a bit different than what I've done before (used nearest neighbour vectors and a DFT instead of what I will show below), I'm not quite sure how ...
2
votes
0answers
346 views

A question about Dirac operator

The Dirac operator at 2 dimension can be written as $$ D=\sum_{k=1,2}\sigma^{k}D_{k}=\left( \begin{array}{cc} 0 & \partial_{x}-i\partial_{y}-i(A_x-iA_y)\\ ...
5
votes
2answers
517 views

effective theory of graphene

This is a question about deriving effective mass theory for graphene. For the two sub-lattice atoms, the wave equation can be written as the massless Dirac equation: $ \displaystyle -i\hbar v_F ...
5
votes
1answer
370 views

What is the boundary condition of graphene flake with zigzag edges?

It is a question about free carrier behavior in graphene flakes. (or may be called charge confinement) Say if we have a perfect hexagonal free standing graphene flake terminated with zigzag edges. ...
8
votes
2answers
1k views

How do Dirac fermions arise in graphene, and, what significance (if any) does this have for high-energy physics?

Graphene has a honeycomb lattice (in the absence of defects and impurities). By considering the low-energy limit of the half-filled Hubbard model used to model the strongly interacting electron gas we ...